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Jul 30, 2017 at 19:19 comment added Markus Scheuer @Drew: No worries. Good that your question could be answered and thanks for the info.
Jul 25, 2017 at 22:55 comment added Drew I omitted a factor of $\binom{n-1}{n_1}$ right after the first summation. That is probably causing the discrepancy. Sorry about that! I did get an answer to my original (linked) question, so that also answers this one.
Jul 16, 2017 at 21:35 comment added მამუკა ჯიბლაძე The table of lhs-rhs shows growing discrepancy,$$ \begin{array}{ccccc} -1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 \\ 0 & -2 & 0 & 2 & 0 \\ 2 & -8 & 12 & -8 & -30 \\ 39 & -61 & 6 & -122 & 195 \\ \end{array}$$
Jul 16, 2017 at 21:31 history edited Markus Scheuer CC BY-SA 3.0
formatting improved
Jul 16, 2017 at 21:20 history answered Markus Scheuer CC BY-SA 3.0